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Cyril Thereau - handed his first league start by Andrea Stramaccioni - vindicated his coach's decision by netting the only goal of the game on 26 minutes to leave Udinese three points adrift of co-leaders Juventus and Roma.
Lazio started the better of both sides and should have moved ahead after the 20-minute mark, having missed two good opportunities.
Both opportunities proved costly shortly after, as Thereau latched on to Silvan Widmer's through-ball before thrashing into the roof of the net to give the visitors the lead.
Stramaccioni's side might have doubled their advantage three minutes after the break, with Panagiotis Kone firing over the bar from close range following a mazy run.
Both sides cancelled each other out for the remainder of the half as Lazio failed to fashion the goalscoring chances necessary to draw level.